How do you use implicit differentiation to find y' for sin(xy) = 1

Iris Vaughn

Iris Vaughn

Answered question

2022-10-14

How do you use implicit differentiation to find y for sin ( x y ) = 1 ?

Answer & Explanation

Crubery3

Crubery3

Beginner2022-10-15Added 6 answers

By implicit differentiation, we can find
y = 1 x cos ( x y ) - y x
Let us work through it.
sin ( x y ) = 1
by implicitly differentiating with respect to x,
cos ( x y ) ( 1 y + x y ) = 1
by dividing by cos ( x y )
y + x y = 1 cos ( x y )
by subtracting y
x y = 1 cos ( x y ) - y
by dividing by x
y = 1 x cos ( x y ) - y x

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